If each of the two digits X and Y is distinct

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If each of the two digits X and Y is distinct

by VJesus12 » Sat Aug 25, 2018 1:50 am

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If each of the two digits X and Y is distinct, is the two-digits integer XY prime?

(1) Each of the digits X and Y is the sum of 2 distinct single digit prime numbers.

(2) The sum of digits X and Y is 16.

The OA is the option B.

I need some help here. Could anyone clarify this DS question to me? I don't know how to solve it. <i class="em em-confused"></i>

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 25, 2018 1:50 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 25, 2018 5:47 am

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VJesus12 wrote:If each of the two digits x and y is distinct, is the two-digit integer xy prime?

(1) Each of the digits x and y is the sum of 2 distinct single digit prime numbers.
(2) The sum of digits x and y is 16.

Target question: Is the two-digit integer xy prime?

Given: Each of the two digits x and y is distinct

Statement 1: Each of the digits x and y is the sum of 2 distinct single digit prime numbers.
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 + 5 = 8 and y = 2 + 7 = 9. So, xy = 89. In this case, the answer to the target question is YES, xy IS prime
Case b: x = 2 + 7 = 9 and y = 3 + 5 = 8. So, xy = 98. In this case, the answer to the target question is NO, xy is NOT prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of digits x and y is 16
Since x and y are DISTINCT, there are only 2 possible ways to get a sum of 16. Let's examine each possible case:
Case a: x = 7 and y = 9. So, xy = 79. In this case, the answer to the target question is YES, xy IS prime
Case b: x = 9 and y = 7. So, xy = 97. In this case, the answer to the target question is YES, xy IS prime
Since each possible case yields the SAME answer to the target question, it MUST be the case that xy IS prime
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com